Question: Simplify the following expression: $r = \dfrac{-2t^2 - 28t - 96}{t + 6} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-2$ , so we can rewrite the expression: $ r =\dfrac{-2(t^2 + 14t + 48)}{t + 6} $ Then we factor the remaining polynomial: $t^2 + {14}t + {48} $ ${6} + {8} = {14}$ ${6} \times {8} = {48}$ $ (t + {6}) (t + {8}) $ This gives us a factored expression: $\dfrac{-2(t + {6}) (t + {8})}{t + 6}$ We can divide the numerator and denominator by $(t - 6)$ on condition that $t \neq -6$ Therefore $r = -2(t + 8); t \neq -6$